Simplify to lowest terms. $\dfrac{108}{120}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 108 and 120? $108 = 2\cdot2\cdot3\cdot3\cdot3$ $120 = 2\cdot2\cdot2\cdot3\cdot5$ $\mbox{GCD}(108, 120) = 2\cdot2\cdot3 = 12$ $\dfrac{108}{120} = \dfrac{9 \cdot 12}{ 10\cdot 12}$ $\hphantom{\dfrac{108}{120}} = \dfrac{9}{10} \cdot \dfrac{12}{12}$ $\hphantom{\dfrac{108}{120}} = \dfrac{9}{10} \cdot 1$ $\hphantom{\dfrac{108}{120}} = \dfrac{9}{10}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{108}{120}= \dfrac{2\cdot54}{2\cdot60}= \dfrac{2\cdot 2\cdot27}{2\cdot 2\cdot30}= \dfrac{2\cdot 2\cdot 3\cdot9}{2\cdot 2\cdot 3\cdot10}= \dfrac{9}{10}$